Force due to: top wire having a magnetic field, bottom wire is in the field, bottom wire feels force due to F=BILsinx (and same true but with bottom wires magnetic field)

Use FLHR to determine the direction of the resultant force

By Newton's 3rd law two parallel wires carrying a current in the same direction experience an attractive force

Ampere definition; The ampere is the current that flows through two infinite, thin parallel wires, one metre apart in vacuum, producing a force between the wires of exactly 2x10^-7 N per metre of length

Ion Beams and Accelerators

First particle accelerator just a glass tube, cathode and anode

Uniform electric field between cathode and anode which accelerates the electrons with force: F=Eq

Electron-volt (eV)

Energy transferred when an electron moves between two points with a potential difference of 1 volt between them (1eV = 1.6 x 10^-19 J)

For an electron being accelerated, its the KE acquired when accelerated through a pd of 1V

You can have a vertical electric field as well as a horizontal one to deflect the electrons further and cause them to also experience a constant force downwards of F=Eq

Linear accelerator (Linac)

Series of tubes charged either +ve or -ve depending on alternating pd sent to them

First tube -ve so proton attracted to it

When protons gets inside tube, no force acting on it so pd changes and tube in front is -ve, which attracts it

Electric field always accelerates it to the right

Pd must be synchronised to proton always inside tube when pd changes

Achieved by keeping frequency constant but increasing lengths of tubes and gaps between them as proton moves faster

Cyclotron

Acceleration provided by electric field

As proton is in gap between to Dees (semi-circular plates) it's accelerated across the gap by an electric field

Magnetic field keeps proton in circular motion

But as speed increases so does radius of circle

Proton eventually spirals out and leaves the cyclotron

Frequency is constant because B-field is uniform and q and m are both constant in equation: f=(Bq)/(2pim)

Frequency stays the same even as velocity increases

Synchrotron

Speed increase provided by an alternating pd

Charged particle performs circular motion due to B-field

Acceleration occurs 4 times per orbit, when the particles cross between the differently charged tubes

Radius of orbit remains constant, so B-field must increase as particle moves faster and frequency increases as particle moves faster

Electromagnetic Induction

Magnetic Flux

Magnetic flux = AB cosx

A is the area, B is the B-field and x is the angle between the B-field and the angle between the normal to the surface and the B-field

Unit is the Weber (Wb)

B-field is the magnetic flux divided by the area, it's the magnetic flux density

Flux Linkage

Magnetic flux referring to many loops rather than just one

If a coil has N loops and the magnetic flux through each loop is *phi*

Total magnetic flux for whole coil is: N*phi*=BAN

Unit is Weber-turn

Faraday's Law

The induced EMF is equal to the rate of change of flux linkage

V = (BAN) / t

Two ways of inducing EMF from Faraday's Law

1. By varying the B-field

2. By varying the area - through some sort of motion

How does a transformer work using Faraday's law?

1. Alternating current in primary coil provides alternating magnetic field inside it

2. Magnetic field lines follow iron sore to secondary coil

3. Magnetic field inside seconary coil is alternating because the current in the primary is alternating

4. An alternating EMF is induced in the secondary coil because of the changing flux linkage according to Faraday's Law

Lenz's Law

If an induced current flows due to a change in magnetic flux linkage, then this current will oppose whats causing the current

Its the reason why there's a minus sign in Faraday's law

Rotating a coil in a magnetic field

Coil Position

In some positions, the induced EMF is zero because the coil is not cutting any lines of magnetic fliux

Or the flux linkage of the coil is a maximum because cosx =1 so rate of change of flux linkage is zero

In other positions the induced EMF is a maximum because the coil is cutting lines of magnetic flux at right angles, so cutting lines at the greatest rate

Or the flux linkage of the coil is changing at the greatest rate because cosx=0

Flux Density

Induced EMF proportional t strength of B-field

Stronger B-field results in more lines of magnetic flux being cut

Or a stronger B-field results in a larger magnetic flux linkage for the coil

Coil Area

The induced EMF is proportional to the coil area

A larger area results in more lines of magnetic flux being cut

A larger area results in a larger magnetic flux linkage for the coil

Angular Velocity

Induced EMF is proportional to the angular velocity

As angular velocity increases the rate of cutting of flux increases

As angular velocity increases the rate of change of flux linkage increases